Algebra Examples

$\frac{\frac{n}{12} - \frac{2}{9}}{\frac{n}{6}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{n}{12} - \frac{2}{9}) \frac{6}{n}$

Step 2

To write $\frac{n}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{n}{12} \cdot \frac{3}{3} - \frac{2}{9}) \frac{6}{n}$

Step 3

To write $- \frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{n}{12} \cdot \frac{3}{3} - \frac{2}{9} \cdot \frac{4}{4}) \frac{6}{n}$

Step 4

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{n}{12}$ by $\frac{3}{3}$ .

$(\frac{n \cdot 3}{12 \cdot 3} - \frac{2}{9} \cdot \frac{4}{4}) \frac{6}{n}$

Step 4.2

Multiply $12$ by $3$ .

$(\frac{n \cdot 3}{36} - \frac{2}{9} \cdot \frac{4}{4}) \frac{6}{n}$

Step 4.3

Multiply $\frac{2}{9}$ by $\frac{4}{4}$ .

$(\frac{n \cdot 3}{36} - \frac{2 \cdot 4}{9 \cdot 4}) \frac{6}{n}$

Step 4.4

Multiply $9$ by $4$ .

$(\frac{n \cdot 3}{36} - \frac{2 \cdot 4}{36}) \frac{6}{n}$

Step 5

Combine the numerators over the common denominator.

$\frac{n \cdot 3 - 2 \cdot 4}{36} \cdot \frac{6}{n}$

Step 6

Simplify the numerator.

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Step 6.1

Move $3$ to the left of $n$ .

$\frac{3 \cdot n - 2 \cdot 4}{36} \cdot \frac{6}{n}$

Step 6.2

Multiply $- 2$ by $4$ .

$\frac{3 n - 8}{36} \cdot \frac{6}{n}$

Step 7

Simplify terms.

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Step 7.1

Cancel the common factor of $6$ .

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Step 7.1.1

Factor $6$ out of $36$ .

$\frac{3 n - 8}{6 (6)} \cdot \frac{6}{n}$

Step 7.1.2

Cancel the common factor.

$\frac{3 n - 8}{6 \cdot 6} \cdot \frac{6}{n}$

Step 7.1.3

Rewrite the expression.

$\frac{3 n - 8}{6} \cdot \frac{1}{n}$

Step 7.2

Multiply $\frac{3 n - 8}{6}$ by $\frac{1}{n}$ .

$\frac{3 n - 8}{6 n}$